Exact sequence of semistable vector bundles on algebraic curves

TL;DR

This paper establishes the existence of specific short exact sequences of semistable vector bundles on algebraic curves, introducing a novel method applicable under certain slope conditions for curves of genus at least one.

Contribution

It provides a new approach to constructing exact sequences of semistable vector bundles on algebraic curves with particular geometric conditions.

Findings

Existence of exact sequences under slope conditions

New method for proving vector bundle properties

Applicable to bielliptic and general moduli curves

Abstract

Let X be a smooth complex projective curve of genus g bigger or equal to 1. If g is bigger than 1 assume further that X is either bielliptic or with general moduli. Under a natural condition on slopes, we prove that there exists a short exact sequence of semistable vector bundles with given ranks and degrees. The importance of the paper consists of the new method adopted for the proves.